# Posterior Regularization on Bayesian Hierarchical Mixture Clustering

arXiv: https://arxiv.org/abs/2105.06903 · HTML: https://mlsanity.com/paper/2105.06903/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 43 references that are in the map.
- First posted on arXiv 14 May 2021.

## Builds on (most cited first, 7 of 7)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Bayesian cluster analysis: Point estimation and credible balls](https://mlsanity.com/paper/1505.03339/) (2015)
- [Bayesian Repulsive Gaussian Mixture Model](https://mlsanity.com/paper/1703.09061/) (2017)
- [Optimal Bayesian estimators for latent variable cluster models](https://mlsanity.com/paper/1607.02325/) (2016)
- [Gibbs Max-margin Topic Models with Data Augmentation](https://mlsanity.com/paper/1310.2816/) (2013)
- [Inferring Hierarchical Mixture Structures: A Bayesian Nonparametric Approach](https://mlsanity.com/paper/1905.05022/) (2019)

## Abstract (arXiv)

Bayesian hierarchical mixture clustering (BHMC) improves traditionalBayesian hierarchical clustering by replacing conventional Gaussian-to-Gaussian kernels with a Hierarchical Dirichlet Process Mixture Model(HDPMM) for parent-to-child diffusion in the generative process. However,BHMC may produce trees with high nodal variance, indicating weak separation between nodes at higher levels. To address this issue, we employ Posterior Regularization, which imposes max-margin constraints on nodes at every level to enhance cluster separation. We illustrate how to apply PR toBHMC and demonstrate its effectiveness in improving the BHMC model.